Question

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The total surface area of a cone whose radius is halved and slant height is doubled:-

`\huge \pink{\frak{ Options - }}\\ \large{\tt{ \dashrightarrow 2 \pi r(l + r)}} \\ \large{\tt{ \dashrightarrow \pi r(l + (r)/(4) )}} \\\large{\tt{ \dashrightarrow \pi r(l + r)}} \\ \large{\tt{ \dashrightarrow 2\pi rl}} \\`
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`\large{\sf \gray{ \leadsto Answer \: should \: explain}}` ​

Answer 1

Formula is

`\\ \rm\Rrightarrow TSA=\pi(r+\ell)`

Now

• r is r/2
• l is 2l

`\\ \rm\Rrightarrow TSA=\pi\left((r)/(2)\right)\left((r)/(2)+2\ell\right)`

`\\ \rm\Rrightarrow TSA=(\pi r)/(2)\left((r+4\ell)/(2)\right)`

`\\ \rm\Rrightarrow TSA=(\pi r)/(2)* 2\left((r)/(4)+\ell\right)`

`\\ \rm\Rrightarrow TSA=\pi r(\ell+(r)/(4))`